Solve: `3(2-5x)-2(1-6x)=1`. Check the result.

Answer

To solve the equation \(3(2 - 5x) - 2(1 - 6x) = 1\), we will follow these steps:

### Step 1: Distribute the terms
We need to distribute the numbers outside the parentheses to the terms inside.

\[ 3(2) - 3(5x) - 2(1) + 2(6x) = 1 \]

This simplifies to:

\[ 6 - 15x - 2 + 12x = 1 \]

### Step 2: Combine like terms
Now, we will combine the constant terms and the terms with \(x\).

\[ (6 - 2) + (-15x + 12x) = 1 \]

This simplifies to:

\[ 4 - 3x = 1 \]

### Step 3: Isolate the variable
Next, we will isolate \(x\) by moving the constant term to the right side of the equation.

\[ -3x = 1 - 4 \]

This simplifies to:

\[ -3x = -3 \]

### Step 4: Solve for \(x\)
Now, we will divide both sides by \(-3\) to solve for \(x\).

\[ x = \frac{-3}{-3} \]

This gives us:

\[ x = 1 \]

### Step 5: Check the result
To check if our solution is correct, we will substitute \(x = 1\) back into the original equation.

The original equation is:

\[ 3(2 - 5(1)) - 2(1 - 6(1)) = 1 \]

Calculating inside the parentheses:

\[ 3(2 - 5) - 2(1 - 6) = 1 \]

This simplifies to:

\[ 3(-3) - 2(-5) = 1 \]

Calculating further:

\[ -9 + 10 = 1 \]

This simplifies to:

\[ 1 = 1 \]

Since both sides of the equation are equal, our solution is verified.

### Final Answer:
\[ x = 1 \]

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